What do you call a question at the beginning of a questionnaire?

In a questionnaire for a housing survey, it starts with the following question:

Do you rent the house you are living in?

If the respondent answers "No", move on to the next question.

If the answer is "Yes", say "Thank you" and leave.

This question is like a probing question to know if the tenant is a real owner or a renter. So, what do you call this kind of question? Something like a "test question"?

Solution 1:

Screening questions

According to popular DIY survey sites (here is just one example): Survey Monkey

Screening questions (also known as "screeners") either qualify or disqualify respondents from taking your survey—depending on how they answer. They let you decide who takes your survey based on the target audience you want to hear from.

And according to professional research companies:

In short, screening questions are placed at the beginning of a survey to determine who is – and isn’t – the right fit for a particular study. Those who “pass” the screener take the actual survey. Those who don’t, well, they are thanked and go on to help us out another time.

Note that a conditional question and filter questions, mentioned in other answers, are more general cases. A conditional or filter question can be used anywhere in the survey to determine what other questions will be asked or skipped. For example in a household composition survey asks "Are there any children under age 18 in the household?" A "yes" gets the next question "What age is the child?" and a "no" jumps to the next section.